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Total variation approximation for quasi-stationary distributions


Barbour, A D; Pollett, P K (2010). Total variation approximation for quasi-stationary distributions. Journal of Applied Probability, 47(4):934-946.

Abstract

Quasi–stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In this paper, we give biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute.

Abstract

Quasi–stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present problems. In this paper, we give biologically plausible conditions under which the quasi-stationary distribution is unique, and can be closely approximated by distributions that are simple to compute.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2010
Deposited On:27 Dec 2017 15:11
Last Modified:18 Apr 2018 11:49
Publisher:Applied Probability Trust
ISSN:0021-9002
Funders:Schweizerischer Nationalfonds
OA Status:Green
Publisher DOI:https://doi.org/10.1017/S0021900200007270

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